Lattice packings with gap defects are not completely saturated
Metric Geometry
2019-09-16 v1
Abstract
We show that a honeycomb circle packing in with a linear gap defect cannot be completely saturated, no matter how narrow the gap is. The result is motivated by an open problem of G. Fejes T\'oth, G. Kuperberg, and W. Kuperberg, which asks whether of a honeycomb circle packing with a linear shift defect is completely saturated. We also show that an fcc sphere packing in with a planar gap defect is also not completely saturated.
Cite
@article{arxiv.math/0303366,
title = {Lattice packings with gap defects are not completely saturated},
author = {Greg Kuperberg and Krystyna Kuperberg and Wlodzimierz Kuperberg},
journal= {arXiv preprint arXiv:math/0303366},
year = {2019}
}